一种多损失条件风险值的双层规划模型及应用

在两级供应链中制造商与零售商之间的多产品定价与订购问题, 是一个多损失的双层风险决策问题, 可以建立双层规划模型解决. 本文研究了一种多损失条件风险值的双层规划模型, 对于多个损失函数和对应的权值水平, 在给定的置信水平下, 定义了不超过给定损失值的最小风险值(即VaR值)和对应的累积期望损失值(即CVaR损失值) 概念, 然后建立了一个多损失条件风险值的双层规划模型, 该模型的目标是求上下层的多损失CVaR值达最小的最优策略, 我们证明了它可以通过另一个较容易求解的双层规划模型获得最优解. 最后, 给出了两级供应链中多产品的定价与订购的双层条件风险值模型, 通过对2种面包产品销售数据进行计算, 获得了面包制造商的最优批发价和最优回购策略, 及零售商最优订购量.

A bilevel programming of multi-loss conditional value-at-risk model and its applications

Manufacture of multi-product pricing and ordering problem between the supplier and the retailer in a two-stage supply chain is multi-loss of risk decision-making problems, which can establish a bilevel programming model to be solved. This paper first studies a bilevel programming of multi-loss conditional value-at-risk model. For a multi-loss function and the corresponding weight value level, at a given confidence level, we define concept of the loss value does not exceed a given minimum value at risk (VaR) and the corresponding cumulative expected loss value (i.e. the CVaR losses value). Then, we set up a bilevel programming model of the multi-loss conditional value at risk, which the goal of the model is to solve an optimal strategy the minimum CVaR value of this model. This model can be solved more easily through another bilevel programming model to obtain the optimal solution. Finally, a multi-loss conditional value-at-risk model of multi-product pricing and ordering of a two-stage supply chain is presented. Calculated by two kinds of bread product sales data, we obtain a bread manufacturer's optimal wholesale price and optimal repurchase strategy, and retailers the optimal order quantity.